Chris Jennings-Shaffer

Postdoctoral Research
University of Cologne

Contact Information - Research

I am currently a post doctoral scholar, under the mentorship of Kathrin Bringmann, at the University of Cologne.

Contact Information

Office:
E-mail:
Gyrhofstr. 8b
cjenning@math.uni-koeln.de, jennichr@math.oregonstate.edu

Mailing Address:
Mathematical Institute
University of Cologne
Gyrhofstr. 8b
50931 Cologne
Germany

Research

My research interests are centered around integer partitions by q-series, modular forms, harmonic Maass forms, special functions, and combinatorics. In particular I am interested in congruences for partition functions that are not modular forms, introducing new cranks for partition functions, and studying rank functions via harmonic Maass forms. Additionally I enjoy all partition functions and q-series identities coming from Bailey pairs and Bailey's Lemma. I am a strong advocate for explicit computations for conjectures and verifications of theorems. Primarily my computations are done in Maple.

The current version of my CV in pdf format can be found here.

The majority of my articles can be found on arXiv.
Preprints and Submitted Work
  1. Mock modularity of the Md-rank of overpartitions (with H. Swisher)
    submitted for publication ArXiv
Projects in Progress
  1. Asymptotics and Inequalities for the M2-partition Rank Function (with D. Reihill)
Publications:
  1. On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramamunjan's ω(q) (with K. Bringmann and K. Mahlburg)
    accepted for publication in Advances in Mathematics ArXiv
  2. The Generating Function of the M2-rank of Partitions without Repeated Odd Parts as a Mock Modular Form
    accepted for publication in Transactions of the American Mathematical Society (28 pages) ArXiv Maple File
  3. Some Smallest Parts Functions from Variations of Bailey's Lemma
    accepted for publication in Frontiers on Orthogonal Polynomials and q-Series ArXiv
  4. Ranks For Two Partition Quadruple Functions
    accepted for publication in Journal de Theorie de Nombres de Bordeaux, ArXiv
  5. Two Partition Functions with Congruences modulo 3, 5, 7, and 13
    Annals of Combinatorics, Vol. 21 number 3, (2017), pages 397-443 ArXiv
  6. Exotic Bailey-Slater SPT-Functions I: Group A
    Advances in Mathematics, Vol. 305, (2017), pages 479-514 ArXiv
  7. Higher Order Smallest Parts Functions and Rank-Crank Moment Inequalities from Bailey Pairs (with C. Babecki and G. Sangston)
    Research in Number Theory, Vol. 2(1), (2016), pages 1-35 ArXiv
  8. Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E (with F. Garvan)
    Advances in Mathematics, Vol. 299, (2016), pages 605-639 ArXiv
  9. Exotic Bailey-Slater SPT-Functions III: Bailey Pairs from Groups B, F, G, and J
    Acta Arithmetica, Vol. 173 Number 4, (2016), pages 317-364, ArXiv
  10. Overpartition Rank Differences Modulo 7 by Maass Forms
    Journal of Number Theory, Vol. 163, (2016), pages 331-358, ArXiv
  11. Congruences for Partition Pairs with Conditions (formerly titled "Congruences for a Certain Partition Pair by a Crank"),
    Quarterly Journal of Mathematics, Vol. 66, No. 3 (2015), pages 837-860 ArXiv
  12. Rank and Crank Moments for Partitions without Repeated Odd Parts,
    Int. J. Number Theory, Vol. 11, No. 03 (2015), pages 683-703. Arxiv
  13. Higher Order SPT functions for overpartitions, overpartitions with smallest part even, and partitions without repeated odd parts
    Journal of Number Theory, Vol. 149, (2015), pages 285-312. ArXiv
  14. Another SPT crank for the number of smallest parts in overpartitions with even smallest part (formerly titled "Another proof of two modulo 3 congruences and another SPT crank for the number of smallest parts in overpartitions with even smallest part"),
    Journal of Number Theory, Vol. 148, (2015), pages 196-203. ArXiv
  15. The spt-crank for overpartitions (with F. Garvan),
    Acta Arithmetica, Vol. 166, No. 02 (2014), pages 141-188. ArXiv
  16. Hecke-type congruences for Andrews' spt-function modulo 16 and 32 (with F. Garvan),
    Int. J. Number Theory, Vol. 10, No. 02 (2014), pages 375-390. ArXiv
  17. A note on the transcendence of zeros of a certain family of weakly holomorphic modular forms (with H. Swisher),
    Int. J. Number Theory, Vol. 10, No. 02 (2014), pages 309-317.